Problem: $ A = \left[\begin{array}{rrr}3 & 1 & 5 \\ 4 & 5 & 2\end{array}\right]$ What is $ A^{T}$ ?
Solution: To find the transpose, swap the rows and columns. $ A^{T}$ = $\left[\begin{array}{rr}3 & 4 \\ 1 & 5 \\ 5 & 2\end{array}\right]$